Can't see any indication in the 3D view , when changing mesh properties from python console
Make sure you aren't in edit mode. If this is part of a larger script (your example looks like Python Console code), the standard practice is to go into object mode, perform your actions, then enter edit mode again, ie.

import bpy

cube = bpy.context.active_object

# store editor state
is_editmode = (cube.mode == 'EDIT')
if is_editmode:
    bpy.ops.object.mode_set(mode='OBJECT', toggle=False)

# make your changes
cube.data.edges[0].bevel_weight = 1

# restore editor state
if is_editmode:
    bpy.ops.object.mode_set(mode='EDIT', toggle=False)